Is it common to have the client process data in order the lessen the load of the API?

For example, the client sends a request to the API server to retrieve documents / records matching certain filters. Of the matching records, there will be additional processing such as transformations, sorting, etc.

Is it a common design in web development to have the API only return the unprocessed documents / records and then have the client perform the additional processing so that the load on the API is lessen?

It will be decent that you provide closure on all your other open posts.

We would be more incline to help you further.